The First-Passage Approach to Valuing the American Put Option

University of California-Riverside Working Paper 98-03

Posted: 29 Jun 1998

See all articles by David S. Bunch

David S. Bunch

University of California, Davis - Graduate School of Management

Herb Johnson

University of California, Riverside (UCR) - Department of Finance and Management Science

Date Written: February 1998

Abstract

We express the American put price as an integral involving first-passage probabilities. This approach allows us an intuitive interpretation to Merton's result for the perpetual put. We also consider the finite-lived case, derive a differential equation for the critical-stock-price function, and develop candidate analytical solutions that satisfy conditions which occur for short and long times to maturity. We present numerical results demonstrating that these solutions for the critical-stock-price functions and numerical integration of the first-passage probability expression to compute accurate prices for American put options.

JEL Classification: G13

Suggested Citation

Bunch, David S. and Johnson, Herbert E., The First-Passage Approach to Valuing the American Put Option (February 1998). University of California-Riverside Working Paper 98-03, Available at SSRN: https://ssrn.com/abstract=102955

David S. Bunch

University of California, Davis - Graduate School of Management ( email )

One Shields Avenue
Davis, CA 95616
United States
530-752-2248 (Phone)

Herbert E. Johnson (Contact Author)

University of California, Riverside (UCR) - Department of Finance and Management Science ( email )

900 University Avenue
Riverside, CA 92521
United States
909-787-2932 (Phone)
909-787-2933 (Fax)

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